THE NUMERICAL SOLUTION OF NONLINEAR OPTIMAL CONTROL PROBLEMS BY USING OPERATIONAL MATRIX OF BERNSTEIN POLYNOMIALS

A numerical approach based on Bernstein polynomials basis is presented to unravel optimal control of nonlinear systems. The operational matrices of differentiation, integration, and product are introduced. Then, these matrices are implemented to decrease the solution of the nonlinear optimal control problem to the solution of the quadratic programming problem which can be solved with many algorithms and softwares. This method is easy to implement with an accurate solution. Some examples are included to demonstrate the validity and applicability of the technique.